A maximum pseudo-likelihood approach for estimating species trees under the coalescent model

By Liang Liu, Lili Yu, S. Edwards. BMC Evolutionary Biology, 2010

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BackgroundSeveral phylogenetic approaches have been developed to estimate species trees from collections of gene trees. However, maximum likelihood approaches for estimating species trees under the coalescent model are limited. Although the likelihood of a species tree under the multispecies coalescent model has already been derived by Rannala and Yang, it can be shown that the maximum likelihood estimate (MLE) of the species tree (topology, branch lengths, and population sizes) from gene trees under this formula does not exist. In this paper, we develop a pseudo-likelihood function of the species tree to obtain maximum pseudo-likelihood estimates (MPE) of species trees, with branch lengths of the species tree in coalescent units.ResultsWe show that the MPE of the species tree is statistically consistent as the number M of genes goes to infinity. In addition, the probability that the MPE of the species tree matches the true species tree converges to 1 at rate O(M-1). The simulation results confirm that the maximum pseudo-likelihood approach is statistically consistent even when the species tree is in the anomaly zone. We applied our method, Maximum Pseudo-likelihood for Estimating Species Trees (MP-EST) to a mammal dataset. The four major clades found in the MP-EST tree are consistent with those in the Bayesian concatenation tree. The bootstrap supports for the species tree estimated by the MP-EST method are more reasonable than the posterior probability supports given by the Bayesian concatenation method in reflecting the level of uncertainty in gene trees and controversies over the relationship of four major groups of placental mammals.ConclusionsMP-EST can consistently estimate the topology and branch lengths (in coalescent units) of the species tree. Although the pseudo-likelihood is derived from coalescent theory, and assumes no gene flow or horizontal gene transfer (HGT), the MP-EST method is robust to a small amount of HGT in the dataset. In addition, increasing the number of genes does not increase the computational time substantially. The MP-EST method is fast for analyzing datasets that involve a large number of genes but a moderate number of species.

Subfields: Genetics, Molecular Biology, Paleontology

View Paper: https://www.semanticscholar.org/paper/26f737058a0e0cb718156c4e61267b88b326f853

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Citations in the corpus

Fast Coalescent-Based Computation of Local Branch Support from Quartet Frequencies (2016, methodology): “…of MLBS support values as a measure of accuracy in simulation studies, and documented both under-estimation and over-estimation of support (for low- and high-support branches, respectively) using MP-EST (Liu et al. 2010) and supertree methods such as MRP (Ragan 1992) and MRL (Nguyen et al. 2012).”
ASTRAL-III: polynomial time species tree reconstruction from partially resolved gene trees (2018, methodology): “The original analyses on this dataset [5, 33] report that MP-EST [17] run on 14,446 gene trees produces a tree that conflicts with strong evidence from the literature and other analyses on the same dataset.”
Orthology Inference in Nonmodel Organisms Using Transcriptomes and Low-Coverage Genomes: Improving Accuracy and Matrix Occupancy for Phylogenomics (2014, methodology): “2009) and MP-EST (Liu et al. 2010) assume that coalescence is the only source of gene tree discordance, making bootstrap numbers derived from these models difficult to interpret.”
High-Throughput Genomic Data in Systematics and Phylogenetics (2013, methodology): “…ARI 29 October 2013 10:2 Heled & Drummond 2010), directly from biallelic markers (SNAPP: Bryant et al. 2012), indirectly from a set of gene trees (e.g., STEM: Kubatko et al. 2009; MP-EST: Liu et al. 2010), or indirectly using summary statistics (e.g., STAR, STEAC: Liu et al. 2009).”
Quartet Inference from SNP Data Under the Coalescent Model (2014, neutral): “The most popular approaches in this category are Maximum Tree (Liu et al. , 2009b) [also implemented in the program STEM (Kubatko et al. , 2009)], STAR (Liu et al. , 2009c), STEAC (Liu et al. , 2009c), MP-EST (Liu et al. , 2010) and Minimize Deep Coalescences [as implemented in the program PhyloNet ”
Phylogenomic analyses of species relationships in the genus Sabal (Arecaceae) using targeted sequence capture (2016, methodology): “We used STAR (Liu et al., 2009) and MP-EST (Liu et al., 2010) to estimate species trees from the nuclear gene trees, with bootstrap tree re-sampling invoked by each program.”
ASTRAL: genome-scale coalescent-based species tree estimation (2014, methodology): “While several methods are established to be statistically consistent under the multi-species coalescent model, MP-EST (Liu et al ., 2010) and the population tree returned by BUCKy (Larget et al ., 2010) are among the leading methods.”
StarBEAST2 Brings Faster Species Tree Inference and Accurate Estimates of Substitution Rates (2016, methodology): “These include summary methods which utilize distributions of estimated gene tree topologies as input, such as the rooted triplet method MPEST (Liu et al. 2010) and the quartet method ASTRAL (Mirarab et al.”
RASP 4: ancestral state reconstruction tool for multiple genes and characters. (2019, positive): “In RASP, users can compute trees distances using different methods: KC distance (Kendall and Colijn 2016), triplet distance implemented in mp-est (Liu, et al. 2010), RF distance (Robinson and Foulds 1981), KF distance (Kuhner and Felsenstein 1994), path differences (Steel and Penny 1993), and SPR…”
Inferring Phylogenetic Networks with Maximum Pseudolikelihood under Incomplete Lineage Sorting (2015, methodology): “Extending our approach to higher level networks, with or without ILS, will require extensive theory to work around this lack of identiﬁability.”
New insights into New World biogeography: An integrated view from the phylogeny of blackbirds, cardinals, sparrows, tanagers, warblers, and allies (2015, neutral): “Liu, L., L. Yu, and S. V. Edwards (2010).”